THE EFFECT OF INFLATION
ON INTEREST RATES
by
Paul Wesley Calvert
A thesis submitted in partial fulfillment
of the requirements for the degree
of
Master of Science
in
Applied Economics
MONTANA STATE UNIVERSITY
Bozeman, Montana
June 1988
ii
Approval
of· a thesis submitted by
Paul Wesley Calvert
This thesis has been. read by each member of the author's graduate
committee and has been found to be satisfactory regarding content,
English usage, format, citations, bibliographic style, and consistency,
and is ready for submi~sion to the College of Graduate Studies.
Date
Chairperson, Graduate Committee
Approved for the Major Department
Date
Head, Major Department
Approved for the College of Graduate Studies
Date
Graduate Dean
iii
STATEMENT OF PERMISSION TO USE
In presenting this thesis in partial fulfillment of ·the requirements for a master's degree at Montana State University, I agree that
the Library shall make it available to borrowers under rules of the
Library.
Brief quotations from this paper are allowable without special
permission, provided that accurate acknowledgement of source is made.
Permission for extensive quotation from or reproduction of this
paper may be granted by my major professor, or in his absence, by the
Dean of Libraries when, in the opinion of either, the proposed use of
the material is for scholarly purposes.
Any copying or use of the
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Signature
-----------------------------------Date
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iv
ACKNOWLEDGEMENTS
I would like to thank Drs. Myles Watts and Ronald Johnson for their
helpful comments and criticisms of early drafts of this thesis, and Ms.
Judy Harrison for her help in typing, revising and page layout.
I would
especially like to thank Dr. Douglas Young for the encouragement,
direction, time and effort spent reviewing the research and early drafts
of this thesis.
Although I have received much help in the preparation of this
paper, I claim all errors herein as my own.
v
TABLE OF CONTENTS
Page
..............................................
OF PERMISSION TO USE. ....................................
iii
ACKN'OWI..EDGEMENTS • ••••••••••••••••••••••••••••••••••••••••••••••••••
iv
TABLE OF CONTENTS • ......••••••..•....••.••...•.............•.......
v
LIST OF TABLES . ...... ~ ••••••.••...•..•.••..••••.....••....•...•..•.
vi
ABSTRACT • •••..•••.•••••••••••••••••••••.••••.•••••••••••.•••••.•...
vii
APPROVAL •••••.•••••••
STATEMENT
ii
CHAPTER:
1.
INTRODUCTION AND REVIEW OF THEORETICAL LITERATURE •••••..•..••
Summary of Theoretical Literature on the Effect
of Inflation on Nominal Interest Rates ••.••••••••
1
9
Other Considerations in Modeling Interest Rate
J?etermination . .................................. .
10
2.
REVIEW OF EMPIRICAL LITERATURE.
13
3.
PROPOSED MODEL . •••••••••••••••••••••••••••.••••••••••••••.•••
23
4.
MODEL ESTIMATION • .•...•..•....•••..•••..•...............•....
29
5.
CONCLUSION • ••••.•••••.•.••••••.••••••••..••••••••••••••.•••.•
36
BIBLIOGRAPHY. . . . . • . . . . • . . . . . . . . . . . . . .. . . . . . • • . . . • . . . . • . . . . . . • . . • • . . ..
39
.APPEND IX. • • • • • • • • • . . . . • . . • • • • • • • • • . • . • . . • • • • • • • • • • • • • • . • • . . • • • . . • . .
42
vi
LIST OF TABLES
Table
1.
2.
3.
4.
Page
Estimated coefficients and t~ratios for
1955-I to 1984-IV ......................................... .
30
Estimated coefficients and t-ratios for
1968-I to 1984-IV ......................................... .
31
Estimated coefficients and t-ratios for
1959-II to 1981-IV ........................................ .
32
Comparison of coefficients to those of
other researchers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
vii
ABSTRACT
This thesis addresses the effect of expected inflation on interest
rates, and in so doing attempts to., replicate the findings of John Makin.
In order to obtain an unbiased estimate of the effect of expected
inflation on interest rates, other variables, such as inflation
uncertainty, Federal budget deficits, the state of the business cycle
and Federal Reserve policy, were included in the model. The model is a
reduced form, modified IS-LM macroeconomic model with a money sub-model
to separate expected from unexpected monetary policy.
The regressions showed that a 1% change in expected inflation
causes about a .915% change in short-term Treasury Bill yields; however,
the results depend on the sample period and heteroscedasticity
.correction employed. The point estimate of .915 for the expected
inflation coefficient is similar to what many researchers have
estimated. The coefficients for inflation uncertainty, the Federal
budget deficits, and the business cycle were not significant.
The attempt to replicate the results of John Makin was not
successful. The R2 and coefficients for expected inflation and
inflation uncertainty were different; however, the coefficients for
unexpected monetary policy and the intercept term were quite similar.
1
CHAPTER 1
INTRODUCTION AND REVIEW OF
THEORETICAL LITERATURE
The recent high and volatile interest rates experienced in the U.S.
have raised new questions about the causes of interest rate movements.
Understanding how interest rates are determined is important to both the
public and private sectors.
It is important to the public sector so
policy makers can better understand the expected costs, benefits, and
effectiveness of various fiscal and monetary policies.
Understanding of
interest rate movements is also helpful to business planners, especially
in capital intensive industries.
The purpose of this paper is to
contribute to the understanding of the effects of inflation and other
variables on interest rates.
This paper is divided into five chapters.
The first chapter
contains the introduction and the review of theoretical literature,
while the second chapter covers the empirical literature.
Chapter 3
presents the model, with the estimation results and hypothesis testing
shown in Chapter 4.
The conclusion is in Chapter 5.
One of the earlier investigations of the determinants of interest
rates was performed by Irving Fisher.
Many of the .theories developed in
his book, The Theory of Interest, are still widely respected today and
are used as a standard framework to compare more modern theories.
2
One interpretation of Fisher is that the rate of interest is the
price of current goods compqred to future goods.
Anything that affects
time preference or the future value of goods may have an effect on
interest rates.
Fisher went into great detail explaining factors which
influence people to borrow or lend, but here his conclusions will only
briefly be summarized.
The variables Fisher identified that affect how people decide to
borrow or lend are the size, time-path, and risk of their incomes, and
personal characteristics such as self-control, habit, etc. (Fisher,
1930, pp. 72, 73 and 77).
The individual is assumed to construct the
"·maximum total desirability" (Fisher, 1930, p. 122) income stream by
borrowing or lending.
The person who has the smaller, faster
increasing, less risky income stream is more likely to be a borrower;
the person with the larger, decreasing, more risky income stream is more
likely to be a lender.
Fisher acknowledged that there is another factor in the demand for
loanable funds,·for investment purposes, that affects the interest rate.
"If, then, I am asked to which school I belong •• , time preference or
productivity--! answer 'to both'" (Fisher, 1930, p. 182).
The market
will equate personal time preference to the .marginal return to capital;
both are determinants of interest rates.
The interest rates discussed here have been real, as opposed to
nominal rates.
Fisher wrote that the figure "expressing the rate of
interest in terms of money does depend upon the monetary standard
employed" (Fisher, 1930, p. 36).
If the value, in terms of goods, of
the currency stays constant, then the real and nominal interest rates
will be the same.
When the value of the currency is not stable, "the
rate of interest takes the appreciation and depreciation into account to
some extent, but only slightly
1930, p. 43).
and~
in general, indirectly" (Fisher,
Thus, according to Fisher, inflation has a positive, but
less than a one-for-one, effect on nominal interest rates.
This also
implies that inflation would have a negative effect on real rates.
This
relationship between inflation (p), real (r), and nominal rates (i),
i=r+p, has become known as the
~isher
equation and is the starting point
for most researchers studying interest rates.
Much later Mundell (1963) and Tobin (1965) suggested another
relationship between the real interest rate and the inflation rate.
Tobin argued that an increase in inflation increase.s the real cost of
ho~ding
money, encouraging households to hold a smaller share of their
wealth in money and a larger share in real capital.
This increased real
investment pushes down the marginal product of capital until a new
equilibrium, with a lower real rate, is reached.
Mundell's hypothesis was based on the fact that a rise in the rate
of inflation more quickly reduces the real value of the share of the
individuals' wealth held in cash.
Individuals are then assumed to raise
their rate of saving to obtain a new cash to tangible asset ratio.
This
increase in saving will increase the capital stock and reduce the real
rate of interest.
The Mundell-Tobin effect wouldn't have a large effect
on interest rates since few people store their wealth in cash •. In
modern economies, cash is used as a short-term financial instrument
rather than a store of value.
4
In 1975, Michael Darby extended the Fisher hypothesis to include
taxes.
The tax rules employed by Darby are a crude simplification of
the U.S. tax code.
He assumes proportional income taxes on nominal
interest income at rate t, and allows interest payments to be deductible.
The real after-tax costs and receipts (r*) of a loan are then
r*=i(l-t)-p.
Under this tax system if p rises by one percentage point,
the nominal interest rate must increase by 1/(l~t) percentage points to
keep the after-tax real rate constant.
The required nominal return must
increase by more than the inflation rate because the inflation component
of the interest rate is taxed.
The Darby article is notable because of its introduction of taxes
into the analysis of the determinants of interest rates.
One difference
in Darby's paper as compared to Fisher's work is that Darby assumes the
after tax real rate to be constant where Fisher reported finding a
negative correlation between the real rate and the rate of inflation.
The negative correlation between the real rate and inflation would
reduce Darby's estimate of di/dp by (ar/ap)/(1-t).
In 1976 and 1982, Gandolfi made improvements in the Darby hypothesis by including capital gains taxes and the elasticity of the supply
and demand for loanable funds.
Gandolfi's model assumes that the demand
for loans is a decreasing function of the real after-tax cost of the
loan, and that the supply of money for loans is an increasing function
of the real after-tax return to savers [r*=(l-t)i-p].
Business people
will invest in new capital until the after-tax return, [(1-t)rb], is
equal. to the after-tax real cost of debt financing, [(1-t)i-(1-k)p].
5
The term [(1-t)i-(1-k)p], or rearranged [i-ti-p+kp], is the nominal
interest rate i, less the effect of lower taxes paid due to the interest
deduction ti, less the rate at which the financed asset will appreciate
in nominal terms p, plus the effect of capital gains taxes on the
inflation induced nominal gains kp.
In equilibrium, savings will equal investment at the market
clearing interest rate.
To isolate the effect of a change in the
inflation rate on.the nominal interest rate, the total derivative of
savings (S) with respect to inflation must be set equal to the total
derivative of investment (I) with respect to inflation.
(A)
S(r*) = I(rb)
r*
=
(1-t)i-p
(1-t)rb = (1-t)i-(1-k)p
dS
di
dp = dp
drb
di
dp = dp -
dr* = (l-t) di _1
dp
dp
as
ar*
[ (1-t)
. di
dp -1
di
dp =
3r* -
as
ai
~
~ (1-t)
ar*
1-k
1-t
J = a!: [~! .-(i=~ )]
(1-k)
I=t
di
- arb
According to this equation, the true di/dp will be. between
(1-k)/(1-t) and 1/(1-t).
If the capital gains tax is zero, and if the
supply of savings is perfectly inelastic or elastic, then the Darby
Effect [di/dp=l/(1-t)] will occur.
The Darby Effect will also occur
6
if there is a perfectly inelastic or elastic demand for funds.
The
Fisher Effect (di/dp=l) will occur if the capital gains tax is equal to
the income tax rate and zero.
A more complete investigation into the affect of inflation on
interest rates was undertaken by Feldstein, Green, and Sheshinski
(1983).
They included in their analysis personal and corporate income
taxes, personal capital gains taxes, the decision of firms to issue debt
versus equity, the increasing cost of capital to individual firms, the
depreciation laws that base depreciation expense on historic rather than
economic replacement cost, and the market's demand for debt relative to
capital.
All of these variables have the potential to affect interest
rates and will be covered briefly.
The firm's decision to issue debt or equity is important when tax
laws are designed for an economy with little or no inflation.
As
inflation rises, the relative after-tax cost of different types of
capital changes, and the firm will, subject to the substitutability of
debt and equity in investors' portfolios, find the debt to equity ratio
that minimizes the firm's cost of capital.
Thus the effect of inflation
and taxes on interest rates depends also on how inflation and taxes
affect alternative investments and how investors substitute among
them.
The depreciation laws are important to consider when studying the
effect of inflation on interest rates.
When depreciation is based on
historic cost, and the value of the currency increases o+ decreases, the
present value of the future deductions increases or decreases.
effect, the depreciation laws may subsidize or tax investment.
In
7
All of these effects were accounted for by the authors when they
constructed their estimate for di/dp.
As it turns out, if the firm
finds it advantageous to change its debt to equity ratio, a very complex
expression emerges.
However, if the firm keeps its debt-equity ratio
constant, the expression reduces greatly to (1-g)/(1-t), where tis the
corporate tax rate and g is a cost, proportional to p, that is incurred
if inflation reduces the real value of future tax deductions.
The
authors estimated that the term g is about .20 in the U.S. during the
early 1980's, but would change as the depreciation laws are changed.
The effect of inflation on nominal interest rates is about 20
percent smaller with this analysis than that found by Gandolphi;
however, they are not inconsistent.
The analysis by Feldstein et al.
was of a broader scope and would therefore be expected to produce a more
complex, and hopefully more accurate, conclusion.
A General Equilibrium model was used by Levi and Makin (1978) to
study the Fisher hypothesis.
They claimed that "the Fisher equation
ought to be viewed as a reduced-form relationship derivable from a
simple general equilibrium model" (Levi and Makin, 1978).
The macro-
economic model they employed had commodity, money, and labor markets.
The system of equations that represent these three markets are
differentiated and expressed in elasticity form.
The relationship
i=(r*+p)/(1-t) of the real after-tax (r*) rate, tax rate (t), and
inflation rate (p) was substituted in for the interest rate.
of inflation on nominal interest rates is given by
The effect
8
di
dp
=
1
(1-t) +
Eli([l-Ewp] - Esm)
(i/r*) Enr*([l-Ewp] +1)
The term Eli is the elasticity of demand for money with respect to the
interest rate and Ewp is the short run elasticity of wages with respect
to prices.
Ewp will normally be approximately 1, but in the short run
may be somewhat smaller because of rigidities caused by labor
contracting.
The elasticity of saving with respect to money, Esm, is
assumed to be close to 0 over a long period of time since changes in the
nominal supply of money will not have a lasting real effect on people's
behavior.
Over a short time span this elasticity may be negative
because as new money is put into the hands of individuals, they may feel
wealthier and, at least temporarily, save less.
The after-tax real
interest rate is r*, and Enr* is the elasticity of investment with
respect to the real after-tax interest rate.
For almost all values of Ewp the Darby [1/(1-t)] effect is an overstatement of di/dp.
•
d1/dp
<
>
For (1-Ewp)=O, di/dp < 1/(1-t), for (1-Ewp)<O
1/(1-t) as (1-Ewp)
>
<
Esm.
The authors gave crude estimates for
the parameters included in their estimate of
d~/dp
and found this to
range from .857 to over 1.33, a range which includes many of the
empirical findings.
The authors also noted that as people and institu-
tions learn to contract for labor in a way to keep Ewp closer to 1, the
response of interest rates to inflation will change over time.
The analytical approach in Levi and Makin's paper was first used by
Robert Mundel, but was extended here to include the labor market and the
tax aspects of Darby's paper.
This model suggests some of the dynamics
of interest rate movements not previously discussed in such detail.
The
9
results of this model also suggest, since people don't instantaneously
adjust to financial shocks, that empirical results might not fully
support the theories of Fisher or Darby.
Summary of Theoretical Literature on the Effect
of Inflation on Nominal Interest Rates
Fisher (1930) hypothesized that the nominal interest rate should
take into account the appreciation or depreciation of the currency used
to repay a loan, and reported finding a less than one-for-one change in
the nominal interest rate for a change in the inflation rate.
Darby
(1975) incorporated taxes into the Fisher equation and showed that if
the after-tax real rate were held constant, the nominal rate would vary
1/(1-t) times the inflation rate.
Gandolphi (1976, 1982) pointed out
that Darby's assumption of a constant real rate was really an unrealistic constraint of either an infinitely elastic or inelastic demand curve
or a perfectly elastic or inelastic supply curve for loanable funds.
In
Gandolphi's analysis this constraint was relaxed and it was shown, with
the inclusion of a capital gains tax, to produce an estimate of di/dp
that could range from (1-k)/(1-t) to 1/(1-t).
Felstein et al. (1983)
further broadened the scope of analysis to include corporate income
taxes, the decision of firms to issue debt vs. equity, the increasing
cost of debt to firms, depreciation laws, and the market's demand for
debt relative to equity.
One of the results of their analysis was an
extremely complex equation to describe the effect of inflation on
nominal interest rates.
The assumption of a constant debt to equity
ratio for firms greatly simplified the equation to (1-g)/(1-t) where g
is proportional to inflation and represents the cost associated with the
10
reduced value of future depreciation deductions.
Finally, Levi and
Makin (1978) pointed out that the empirical results of researchers
wouldn't match the theoretical models since they were attempting to
model a dynamic process with a static model.
Other Considerations in Modeling
Interest Rate Determination
Other variables that affect real interest rates that have been used
in empirical studies include government expenditures, government debt,
inflation uncertainty, proxies to measure the demand for private investment demand, monetary policy, and supply shocks.
Government expenditures are occasionally included in reduced form
IS-LM interest rate models because they are considered to be an
exogenous determinant of income and therefore interest rates.
Government debt or deficits are used in some models because they
may affect interest rates, possibly through several channels.
One
channel is that government debt increases the demand for loanable funds
in the capital markets.
In order to maintain equilibrium, the interest
rate must be higher.
Another way that deficits could affect interest rates is that the
Federal Reserve may react to political pressure against high interest
rates caused by the deficit.
The political pressure begins when the
representatives of capital dependent industries lobby Washington for a
reduction in interest rates.
While politicians have no direct influence
on rates, the Federal Reserve Board may not be totally politically
insensitive.
The Board may then increase, or be expected tq increase,
11
the money supply to try to stabilize rising interest rates.
The effects
of monetary policy on interest rates is described below.
The variance of inflation forecasts has been included in some
models as a proxy for inflation uncertainty.
Researchers who have
included this variable into their analysis suggest that greater possibility of higher inflation will cause suppliers of loanable funds to
demand a higher return to compensate for the additional risk.
Inflation
risk is not easy to measure, so instead of using the market's true
distr±bution of expected inflation, a proxy made of the distribution of
inflation forecasts is usually used.
The distribution of inflation
forecasts from different forecasters is not the distribution of the
mark~t's expected inflation, but it does seem likely that the two would
be correlated.
Occasionally some measure of economic activity is used, such as the
difference between current and a past average of unemployment or GNP
growth.
One theory behind these variables is that as capacity becomes a
constraining factor of production, business people will be more likely
to borrow to finance more capacity.
Another theory, but with opposite
implications for interest rates, on why this type of variable should be
included is that as GNP (income) rises above its long-term trend, people
will save more, pushing interest rates lower, for when their income is
lower.
Measures of the money supply have been used in most studies of·
interest rates.
The reason for using it is if the money supply is
changed the loan market will face a shift in supply, which may cause a
change in the interest rate.
The effect of monetary policy on interest
12
rates may depend not only on the actual policy, but on the expected
policy also (Mishkin, 1982).
If people base their actions on their
expectations and their expectations prove incorrect, the resulting
effect could be to change the real interest rate.
A proxy for aggregate supply shock is used in a model by Wilcox.
His theory is that if a country experiences a change in the supply of an
important import, such as oil, the marginal return to capital in general
will be lower.
The decrease in the marginal return to capital will dis-
courage investment and thus cause a downward pressure on interest rates.
In conclusion, these theories together suggest that expected
inflation (Fisher, 1930); taxes (Darby, 1975); the elasticity of supply
and demand for funds (Gandolphi, 1976, 1982) and other variables
(Feldstein et al., 1983); government deficits; inflation uncertainty
(Makin, 1983); expected and actual monetary policy (Mishkin, 1982); and
supply shocks (Wilcox, 1983) may be determinants of interest rates.
The
estimation of the effect of the variables on interest rates is difficult
to measure because people don't immediately adjust to financial shocks
(Levi and Makin, 1973) and their expectations aren't always correct
(Mishkin, 1982).
13
CHAPTER 2
REVIEW OF EMPIRICAL LITERATURE
One of the early empirical studies on the effect of inflation on
interest rates was done by Irving Fisher.
~isher
In The Theory of Interest,
made the distinction between real and nominal interest rates.
Real interest rates were dependent upon many things including, according
to him, institutional influences, laws, politics, banking practices, and
government finance, all of which he thought were worthy of study but
were not within the scope of one book.
The empirical work in The Theory
of Interest centered on the effects of inflation on interest rates.
According to Fisher's findings, which were based mostly on· data in the
u.s.
from 1870-1927, nominal interest rates are slightly responsive to
current price changes, but very responsive to lagged price changes.
The
cumulative effect on interest rates to a 1% change inflation was about
.8, or .9%, which indicates a change in the real rate of .1 or .2% in
the opposite direction of the change in inflation.
Fisher said,
We have found evidence, general and specific, that price
changes do, generally and perceptibly, affect the interest
rate in the direction indicated by a priori theory. But since
forethought is imperfect, the effects are smaller than the
theory requires and lag behind price movements, in some
periods, very greatly (Fisher, 1930).
Lawrence Summers extended the investigation of the effect of inflation on interest rates to the period 1860-1980.
One of the methods used
to test the Fisher hypothesis (meaning a one-for-one increase in
14
interest rates for inflation) was to average inflation rates over the
period of a decade and compare that with the decade long average interest rate.
According to Sunnners, "No clear relationship between
inflation and nominal interest rates emerges" (Sunnners, 1982).
period 1860-1940, he found no support for the Fisher effect.
For the
Regres-
sions of 3-month Treasury Bill yields on inflation for the period 1948
to 1980 yielded different results.
The inflation coefficient was always
positive and significant, but ranged from .29 to .86, depending on which
subperiod and sample frequency was used.
The results rejected the
hypothesis that di/dp=l in 15 of 20 regressions.
In 1976, Thomas Cargill tried to estimate the effect of inflation
on interest rates, but he emphasized the SO's and 60's.
Cargill used
two regression equations, i=a+bp, and i=a+bp+cX+dM, where i is the
3-month, 9-12 month, 3-S year, or long-term government security, a is a
constant, p is the Livingston survey average of expected inflation for 6
or 12 months into the future, and X and M are the percentage change in
real GNP and real money supply,, respectively.
The inflation coefficients from the first model for the SO's were
.64 and .67, and marginally significantly different from 0 for the
shorter maturities but not significantly different from 0 for the longer
two maturities.
For the 60's the inflation coefficients are always
significantly different from 0, even at the 1% level, and their size
ranged from .79 for the long-term rate to 1.18 for the 3-month rate.
The second model produced coefficients for the inflation variable that
are very small, .01 to .21, and not significant for the SO's, but much
15
larger, .80 to 1.08, and very significant for the 60's.
Similar results
have been found by Gibson.
There are two major criticisms of Cargill's regressions.
The first
is the exclusion in the first equation of independent variables other
than expected inflation.
Leaving important variables out of an
estimated equation will probably give biased estimates of the remaining
coefficients.
The second problem is the use of the 12-month expected
inflation series in the regressions of the longer term interest rates
may have caused some problems in interpreting the results.
Theoretically each expected cash receipt from the securities should be
discounted by the expected price index at the time of payment to measure
the effect of inflation on interest rates.
This leaves only the regressions of the second equation with the
shorter-term maturities as least biased.
These regressions show the
interesting results of considerable difference between the effect of
inflation on interest rates in the SO's and 60's.
Research was undertaken by Carlson in the 70's that included an
estimation of the expected real interest rate.
He subtracted the
Livingston survey expected inflation rates from the return on 12-month
Treasury Bills.
The results from 1953 to 1975 showed that this estimate
of the real rate varied from 0 to 4.5%.
"The most notable declines in
nominal interest rates occur in 1953-54, 1957-58, 1960, 1966-67, 196970, and 1974-75.
All of these, with the possible exception of 1966-67,
are associated with recessions" (Carlson, 1977).
These results suggest
that some measure of the performance of the economy should be used in
16
regressions on nominal interest rates to account for changes in the real
rate.
Vito Tanzi (1980) believed that the real rate is variable and
correlated with economic activity.
Because of this, he included a
variable to control for effects of the business cycle on the real rate
when he did regressions with the nominal rate.
The variable he used
that would be correlated with the economy was the GNP gap, which is the
difference between the logs of actual and potential GNP.
The introduction of this economic activity variable into the Fisher
-2
equation gave sharply higher R and the coefficients for the inflation
variables sharply increased to close to 1.
The estimates for expected
inflation were the subsequently observed, distributed lag, adaptive,
extrapolative, and a couple of less well-known types.
on the various expected inflation proxies and the
G~
The coefficients
gap were all
significant at the 1% level.
In conclusion, Tanzi said that since all the coefficients on the
expected inflation proxies were significantly less than 1/(1-t)
(estimated to be 1.47), individuals have been able to "see through the
money veil, ••• however, they have failed to see through the fiscal veil
and thus have suffered from fiscal illusion" (Tanzi, 1980).
One interpretation of this statement is that Tanzi thinks that as
the inflation coefficient approaches one, the market must be adjusting
the nominal rate upward as Fisher's theory would suggest, and when the
coefficient exceeds one, the market is adjusting the nominal rate upward
as Darby's theory would suggest.
It should be noted that a coefficient
17
of less than one could still be consistent with the tax effect suggested
by Darby.
John Makin developed a model to explain 3-month Treasury Bill rates
using a regression equation which includes variables for expected
inflation, surprise money growth, inflation uncertainty, and fiscal
deficits.
The expected inflation proxy came from the Livingston survey
data, as did the inflation uncertainty variable.
Surprise money growth
was defined to be the residuals from an ARMA (0,8) model of Ml growth.
After estimation of the regression parameters, it was found that
the error structure was not well represented by an ARMA (1,0).
Estima-
tion of a transfer function showed that an ARMA (1,1) model was needed
to leave white noise residuals.
The regression results show the coefficient for inflation to be
highly significant and slightly greater than unity, the coefficient for
surprise money growth was very significant and negative, the coefficient
for inflation uncertainty was negative and occasionally significant
depending on the subperiod estimated, and lastly the coefficient for the
deficit was very small and not significant.
The author argues that the
procyclical movement of interest rates, together with the countercyclical cyclical movement of fiscal deficits, will lead to a downwardly
biased coefficient for the deficit.
He further suggests that exports
may be used to measure the shocks on aggregate demand to interest rates.
The effect of exports on interest rates is larger than that of deficits,
but is still not significant.
Some of the main contributions of the Makin article are the use of
the residuals from a money model for the money supply variable, the
18
search for the actual error process rather than assume random or AR-1
errors, and the inclusion of variables for inflationary risk and fiscal
deficits.
These and other ideas are incorporated in a model in this
paper that will be estimated and presented in later chapters.
A different approach was taken by Mishkin to determine what
influences real interest rates.
He regressed the expost real rate of
3-month Treasury Bills on real GNP growth, GNP gap, unemployment, expost
inflation, the investment to capital ratio, and various measures of
money supply growth.
The null hypotheses that the coefficients for the
GNP growth, the GNP gap, the unemployment rate, and the investment to
capital ratio were all equal to zero were not rejected.
The only signi-
ficant variables were the inflation rate and the money growth rates, and
the money variable became insignificant when lagged inflation was
included in the regression.
The author does point out that the real
variables may actually be correlated with the real rate, but that the
statistical tests he used were not powerful enough.
These results of Mishkin's on the significance of economic activity
variables are in contrast to the results reported by Tanzi.
Perhaps
part of the difference is the use of expost real rates as the dependent
variable in Mishkin's regressions.
A model introducing supply shocks was designed by Wilcox in 1983.
The supply shock variable is defined as the deviation from the 1952-79
mean of a ratio of the implicit price deflator for imports to the GNP
deflator.
The idea behind the supply variable was that a change in the
price of an important import, like oil, could change the returns to
capital and therefore cause changes in the interest rate.
19
Other variables were included to control for changes in the money
supply, expected inflation and exogenous demand.
This last variable was
defined as the deviations from the 19S2-79 mean of the sum of real
federal government defense expenditures and real exports, normalized by
natural real output.
The supply variable was significant, and its inclusion keeps the
relationship between inflation and 'interest rates stable during the SO's
and 60's.
Earlier, Cargill reported the different. reltionship between
inflation and interest rates during the SO's and the 60's, but he didn't
include any variables to account for the effect of the world economy on
U.S. interest rates.
As the U.S. economy continues to grow slower than
the world economy, and therefore becomes relatively smaller, it seems
reasonable that international markets will continue to have a greater
effect on U.S. interest rates.
Robert Ayanian (1983) used the tax-free status of municipal bonds
to test the theory that interest rates should vary at rate 1/(1-t) times
the change in the rate of inflation.
Ayanian noted that one problem
previous researchers had in trying to prove this theory was the difficulty in observing the expected real interest or inflation rate.
Both
of these together should be observable as the nominal return on
municipal bonds, he argued.
For the period 19S2-79, taxable bond yields were regressed on taxfree municipals.
The resulting coefficients imply a 1% change in the
tax-exempt yields would result in a 1.63% change in taxable yields,
indicating a marginal tax bracket of 38.7% --proof, the author says, of
the Darby effect.
20
The regression reported by Ayanian is interesting but does not
necessarily prove the Darby effect.
This regression does suggest that
people respond to after-tax rates but the Darby hypothesis held that the
derivative of (r+p)/(1-t) with respect top is (0+1)/(1-t).
Joe Peek (1982) claimed that "the common conclusion that the
empirical evidence did not support the tax-adjusted Fisher hypothesis
was due to the use of .an inappropriate null hypothesis." Peek then
proposed several new ways to test the hypothesis that taxes are important in the determinance of interest rates.
Four models are used in Peek's testing:
a/(1-tax)+b(M~-P~)+cG~+dZ~+eP~
(A)
it
=
(B)
it
= a+b(Mt-Pt)+cGt+dZt+ePt
(C)
i
t
= model (A) plus extra term qFIT(Bt)
(D)
i
t
= model (B) plus extra term qFIT(At)
Where it is the 6- or 12-month Treasury Bill yield, tax is the average
marginal tax rate, Mt is the log of the money supply less the log of
real output, Gt is the log of real government expenditures less the log
of natural real output, Zt is the percentage change in output the
preceding time period, and Pt is the expected inflation rate from either
the Livingston survey, an extrapolative or a rational expectations model
of expected inflation.
The ' marks in model A means that variable was
transformed by dividing by (1-tax).
The first test is to see which model, (A) or (B), has the lower sum
of squared residuals.
In all six models (2 interest rates by 3
inflation proxies), the SSR was smaller for the tax-adjusted model.
As
a second test, the regression equations were estimated for the 1959-76
21
period and used to forecast rates for the 1976-79 period.
The root mean
squared errors were smaller in all instances in the tax-adjusted models.
As a last test, regressions (C) and (D) were estimated, where
FIT(At) and FIT(Bt) are the predicted rates from models (A) and (B),
respectively.
Model (D) is used to test the null hypothesis that taxes
are important and model (C) is used to test the null hypothesis that
taxes aren't important.
If the FIT coefficient is significant, then the
null hypothesis will be rejected.
The results of this last test were that the null hypothesis that
the tax-adjusted equation is the true model is rejected in
six instances.
o~ly
one of
The author says that the one rejection is because of
multicollinearity problems and not because the non-tax adjusted model
was better.
The null hypothesis that the non-tax adjusted model was better was
rejected at the 10% level of confidence in four of the six tries.
The
author concludes that these tests provide very strong evidence that
taxes are important in the analysis of interest rates.
The empirical results of the papers covered here suggest estimates
of the response of interest rates to inflation depend on the sample
period, the maturity of the security, and the variables used to control
for changes in the real interest rate.
The various measures of the
money supply and supply stocks have generally been found to be significant while the federal budget deficit and inflation uncertainty have
not.
Different measures of the level of economic activity, such as the
GNP gap, are found to be significant in some models but not in others.
22
Taxes appear to be significant but the Darby effect [di/dp = 1/(1-t)]
seems to be an overstatement.
Due to the varied results of models that include variables of
control for changes in the real rate, it is suggested that a complete
study should test as many of them as possible.
23
CHAPTER 3
PROPOSED MODEL
The method of this study is three-fold.
First, attempt to
replicate the basic findings of Makin in his August 1983 article in The
Review of Economics and Statistics; second, to make minor modifications
to his model; and finally, to re-estimate his equations with newly
available data.
A modification of the IS-LM model will be combined with a tax
adjusted Fisher equation, much like that used by Makin (1983), to
produce a reduced form equation of nominal rates.
This specification
recognizes inflation, federal budget deficits, the GNP gap, inflation
uncertainty, the
ela~ticity
of supply and demand for funds, and monetary
policy as possible determinants of interest rates as suggested by various authors in the literature review.
Numerical estimates of the effect
of some of the variables such as taxes cannot be explicitly derived from
the equation that will be estimated but are noted as being implicit in
the coefficients that are estimated.
The modifications to the standard IS-LM model are the inclusion of
inflation risk, life-cycle saving, and monetary shock
varia~les.
The inflation risk variables, defined as the standard deviation of
expected inflation as reported by Livingston, are included in both the
investment and savings equations to serve as proxies for risk associated
24
with contracting in nominal rates.
Increased risk would result in a
shift to the left in both the supply and demand schedules for loans.
A life-cycle savings variable is added to account for the effects
on savings of perceived temporary changes in income.
Theory suggests
that as income temporarily increases (decreases), above (below) its long
term trend, savings will increase (decrease) so as to remain close to a
long term, utility maximizing consumption stream.
The monetary shock variable is included because interest rates may
be temporarily affected until the markets adjust to the new quantity of
money.
Another monetary policy variable, Money Expected, is included in
some regressions to highlight the different effects of expected versus
unexpected monetary policy as proposed by Mishkin in the theoretical
literature review.
The structure of the model is as follows:
The IS curve is
constructed by setting the log of real autonomous spending,
equal to the log of the sum of taxes and real saving.
where:
log of real autonomous spending
At
st
= log
rt
= after-tax
var(Pt)
= inflation
Xt
=
a measure of real exogenous expenditure
et
=
normally distributed error term with mean = 0
of real total non-expenditure
real interest rate
uncertainty, measured as the standard
deviation of inflation forecasts
25
yt
= log of real income
ypt
= log of expected permanent real income
pt
= expected inflation
The LM curve is
where:
Mt
= log of actual money supply
Me
t
Ms
t
= log of expected money supply
= money surprise, or (Mt - M~)
is solved for Yt and substituted into the IS curve.
Solving this new
expression for r gives the reduced form equation for after-tax real
interest rates.
The Fisher equation
where:
T
= marginal
T'
=
tax rate on interest income
marginal tax rate on returns from real assets
is used to relate the after-tax real rate to the nominal interest rate.
The resulting equation reduces to
where:
All Vi's have the same common denominator D
D
(l-T)A [1-(S M /M A )]
1
1 1 3 1
v0
=
(A
Vl
=
-M
0
-s 0+M0 S1 /M3 )/D
s
2 1
/DM +(1-T')/(l-T)
3
26
v2
= -s 1 /M3D
v3
=
v4
= A3 /D
vs
= -8 3 /D
v6
=
(S -A )/D
2 2
[(elt-e2t)+(Sle3t/M3)]/D
The size, or even the sign, of v 1 is indeterminant since both a
positive and a negative coefficient enter into its definition.
The
first term of the expression is negative because as inflation rises,
holding other things constant, people will want to hold less cash.
The
second part of the expression indicates that the degree to which
inflation affects interest rates is partly dependent on how real and
financial assets are taxed.
The sign on the unexpected money variable should be negative.
As
the money supply is increased beyond what is expected, the interest rate
should fall because of the greater quantity of money available.
In the
regressions either the money surprise or the money surprise and money
expected variables were included.
The size of the coefficient for money
expected is not anticipated to be significantly different from 0.
The
definition of money surprise was decided to be the residuals from an '
ARMA model of M growth that left white noise residuals.
1
An ARMA (5,0)
model met this requirement.
The coefficient v
3
could be negative or positive.
Increased
inflation risk would induce borrowers to borrow less and/or demand a
lower interest rate.
Lenders, on the other side of the market, would
want a higher interest rate and/or to lend less to compensate them for
27
greater inflation risk.
The net effect on interest rates of increased
inflation risk is not determinable by these theories.
The effect of an increase in exogenous expenditures on interest
rates is positive.
is difficult.
Trying to find a truly exogenous expenditure series
Net exports are used in some models, but net exports are
dependent on the value of the dollar, which is somewhat dependent on
interest rates.
endogenous.
Thus, it appears that net exports are to some extent
In this study, the cyclically adjusted budget deficit as a
percent of trend GNP is used as a measure of exogenous expenditures.
However, the effect of deficits on interest rates is controversial.
Barra (1974) used the bequest motive for explaining how the Ricardian
Equivalence Theorem operates.
This theory suggests that if current
taxes are cut and government spending stays constant, then the current
generation will save the tax cut so they can leave it to their offspring
to pay the future taxes required to repay the bond holders.
This
theory, which suggests that government deficits won't affect interest
rates, is in contrast to the traditional Keynesian position that
government deficits raise interest rates.
The expected sign on the coefficient for the GNP gap, that is the
difference of the logs of current and expected GNP, is uncertain.
As
income rises above what is assumed to be a permanent level of income,
people are presumed to save more to offset years when income is below
what they had expected.
The increased saving should have a depressive
effect on the interest rate.
On the other hand, when income is above
its trendline, manufacturing plants would probably be nearing capacity.
As plants approach capacity, the owners may be likely to borrow more
28
money to finance construction, which would exert a positive influence on
interest rates.
The common denominator of all the Vi's, D, contains the tax term T,
which unfortunately isn't constant over the sample period.
The
denominator D, along with more tax trends in variable Vi, makes
estimation of this model virtually impossible.
The estimation procedure
described later does not address this problem.
In effect, the
simplifying assumption of a constant tax rate is implicitly made.
29
CHAPTER 4
MODEL ESTIMATION
The model developed in the previous section is estimated for three
different time periods with the results shown in Tables 1, 2 and 3.
Table 1 shows the results from the 1955-I to 1984-IV sample period,
Table 2 shows the results from the 1968-I to 1984-IV period, and Table 3
shows the results of the 1959-II to 1981-IV period.
The objective in
choosing the first sample period was to obtain a large sample, but not
to the extreme of including data points when the Federal Reserve Board
pegged the Treasury Bill rates.
The second sample was chosen because
1968 is about the time when inflation became high and highly variable.
The 1968 to 1984 period witnessed the increase and then the decrease of
inflation.
The mid-1980's is the first time in years that researchers
could get data without strong trends in many of the variables.
The
third sample period is the same as Makin's in his article, "Real
Interest, Money Surprises, Anticipated Inflation and Fiscal Deficits,"
and is used in an attempt to duplicate his findings.
The size and sign of the expected inflation coefficient for the
first sample is similar to the results of other researchers such as
Fisher, Cargill, Gibson, and Tanzi.
The coefficient estimate of about
.9 indicates that historically a 1% change in expected inflation has
caused a .9% change in the 3-month Treasury Bill rate.
30
Table 1.
Estimated coefficients and t-ratios for 1955-I to 1984-IV.
Variable Names*
Expected d
Constant
Inflation
Unexpected
Money
Inflation
UncerFederal
tainty
Deficit
2.4lc
(4.98)
.915c
(6.27) (.59)
-.053c
(3.08)
.014
(.04)
2.4lc
(4.95)
.915c
(6.23) (.58)
-.052c
(3 .06)
.014
(.05)
2.36c
(4.94)
.895c
(6.19) (. 72)
-.o5oc
(2.95)
.087
(.28)
2.52c
(4. 96)
.918 c
(6.14) (.55)
-.062c
(3 .01)
.005
(.02)
2.34c
(4.96)
.898c
(6.26) (. 71)
-.o5oc
(2.93)
.082
(. 26)
GNP
Gap
Expected
Money
-.004
(.05)
.049
(1.49)
-.026
(.82)
.015
(.17)
.049
(1.50)
aSignificant at .05 level.
b
Significant at .01 level.
cSignificant at .005 level.
d
The first t-ratio is for null hypothesis di/dp=O, the second t-ratio
is for the null hypothesis di/dp=l.
*See Appendix for estimation details and data sources.
AR-1
R2
.874
(18.79)
.79
.874
(18.66)
.79
.872
(18.59)
.80
.878
(18.93)
• 79
.868
(18.18)
.80
31
Table 2.
Estimated coefficients and t-ratios for 1968-I to 1984-IV.
Constant
Variable Names*
Expected ·unexInflation
Federal
pected
UncerInflaDeficit
tion
Money
tainty
3.2Sc
(2.67)
.544a
(2.02)
-.081a
(2. 08)
.840
(1.33)
3.74c
(3.25)
.515a
(1.83)
-.083a
(2.15)
.878
(1.41)
2.54a.
(2.10)
.sssa
(2.06)
-.072a
(1.89)
1.080a
(1. 72)
2.73a
(2.09)
.568a
(2.09)
-.059
(1.34)
.812
(1. 28)
2.98a
(2.37)
.517a
(1.83)
-.075a
(1.96)
1.082a
(1. 73)
a:·
GNP
Gap
-.217
(1.34)
.185a
(1.67)
.082
(1.04)
-.188
(1.16)
.164
(1.48)
.
Significant at .OS level.
b Significant
Expected
Money
at .01 level.
cSignificant at .005 level.
*See Appendix for estimation details and data sources.
AR-1
R2
.881
(13.86)
.80
.903
(14.93)
.80
.891
(14.14)
.81
.881
(13.49)
.80
.911
(15.08)
.81
32
Table 3.
Constant
Estimated coefficients and t-ratios for 1959-II to 1981-IV.
Expected
Inflation
Variable Names*
Inflation
UnexFederal
pected
UncerMoney
tainty
Deficit
GNP
Gap
Expected
Money
.840a
2.15c
(4 .17)
.669c
(4.09)
-.036a
(1.97)
(1. 70)
2.15c
(4.17)
.670c
(4.08)
-.036a
(1. 96)
.845a
(1.68)
2.09c
(4.23)
.670c
(4.21)
-.035a
(1. 90)
.869a
(1.75)
2.23c
(4.19)
.677c
(4.09)
-.045a
(2.00)
.829a
(1.67)
2.10c
(4.22)
.67lc
(4.21)
-.ossa
(1.89)
.87la
(1.73)
-.012
(.12)
-.031
(.92)
-.024
(. 70)
-.0079
(.08)
-;031
(.91)
AR-1
R2
.84
(13.21)
.75
.84
(13.06)
.75
.83
(12 .51)
.75
.843
(13.11)
.75
.83
(12.35)
.75
.845
(19.1)
.98
Makin Results:
2.06c
(15.80)
1.150c
(5.22)
-.038c
(4.46)
-.217
(1.37)
2.24c
(17.20)
1.058c
(7.33)
-.024c
(3.59)
-.278a
(1.81)
2.19c
(15.57)
1.067c
(7. 25)
-.024c
(3.61)
-.25ld
(1.60)
ARMA (1,1)
.OOle
(1.10)
aSignificant at • 05 level •
b Significant at
.01 level.
cSignificant at .005 level.
d
Makin used the variance of inflation forecasts where this paper
used the standard deviation.
~akin used deficits measured as positive numbers in billions of
dollars at seasonally adjusted annual rates. This paper uses
cyclically adjusted deficits as a percent of trend GNP.
*See Appendix for estimation details and data sources.
.99
33
The coefficient for inflation uncertainty is never significant for this
sample.
The size of the expected inflation coefficient for the second
sample is smaller than other researchers, such as Makin, have found and
the coefficient for inflation uncertainty is much larger.
These
estimates suggest that a 1% change in inflationary expectations causes
about a .5% change in Treasury Bill rates, and that a one standard
deviation increase in the inflation forecasts causes about a .9% change
in Treasury Bill rates.
The point estimates of these coefficients are
not accurate because of multicollinearity problems.
Since inflation and
inflation uncertainty are highly correlated, it is not possible, using
these estimation methods, to accurately estimate their individual
influences on the interest rate.
Estimated coefficients for the expected inflation variable in the
third sample are smaller, but still significant, than in the first
sample and are considerably different than those reported by Makin shown
at the bottom of the page.
The different heteroscedasticity corrections
may account for part of this difference.
All of the data in the Makin
regressions were divided by expected inflation where the data in this
paper were divided by the square root of expected inflation as described
in detail in the appendix.
The coefficient for inflation uncertainty is of different signs in
this paper versus the estimates of Makin.
The coefficient in this paper
is marginally significant at the .OS level with a one-tail t-test and is
marginally significant in the Makin paper only when the regression is
estimated as a transfer function with an ARMA (1,1) model of residuals.
34
In the sample in this study, multicollinearity problems were experienced
which may have led to inaccurate estimates of expected inflation and
inflation uncertainty.
Estimation of the coefficient for money surprise produced a coefficient that is of expected sign for all samples.
The size of the
coefficient is 60% larger in the second sample, but is not as significant.
The second sample coefficient of -.08 means that as the money
supply changes at an annual rate that is 1% different than what was
expected, the Treasury Bill rate has changed in the opposite direction
by .08%.
The same coefficient in the third sample is considerably
smaller but very similar to that published by Makin, even though he used
an ARMA (0,8) model for money where, in the current paper, an ARMA (5,0)
model was used.
A variable described as the expected monetary policy and defined to
be the forecast of the money model was included in both samples to test
the hypothesis that only unexpected government policy will have real
effects on the economy.
In no model specification was the coefficient
significant.
The coefficient for the federal budget deficit is small in the
first and third samples, large in the second, and significant in none.
The size and sign of the variable are interesting in the second sample,
but its significance is rejected even at the 10% level.
The signifi-
cance of this variable is not much different, although of a different
sign, than that found by Makin.
The GNP gap data used in the model is the result of the first stage
regression described in detail in the Appendix.
The variable is
35
marginally significant at the 5-6% level and about three times as large
in the second sample.
The coefficient in the first sample indicates
that if the GNP has been 1% below trend, the interest rate has been
about 5/100% lower than otherwise.·
The coefficient for the same
variable for the second sample indicates that when the GNP has been 1%
below trend, the interest rate has been about 17/100% lower.
The constant for the regressions varies between 2.06 and 3.74,
depending upon model specification and is always significantly positive.
Using the results of the first regression of the first sample, the
equation for the real rate is 2.41 + .915p-p, or 2.41-.0SSp.
It is
apparent from this equation that the real rate is negatively correlated
with inflation and will, if projected beyond the range of the data it
was estimated from, approach 0 as the inflation rate rises above 28%.
36
CHAPTER 5
CONCLUSION
The results of this thesis are that unexpected monetary policy and
expected inflation are significant determinants of interest rates, while
the federal budget deficit, expected monetary policy, and inflationary
uncertainty are not significant, at least as specified in this paper.
The results are mixed with respect to replicating Makin's results.
The
constant and the coefficient for unexpected money are similar to
Makin's, but the coefficients for expected inflation and inflation
2
uncertainty and the R are considerably different.
It was found that
the magnitude of the estimated coefficients vary considerably with
sample period, estimation procedure and the heteroscedasticity
correction employed.
Table 4 shows the Table 1, equation 1 estimates compared to
estimates of other researchers.
There are many areas for improvement in future work of this type,
such as inclusion of taxes and depreciation laws, a better money model,
the development of a dynamic macroeconomic model, and the recognition of
foreign markets.
It may be constructive to explicitly include taxes and/or depreciation laws into the model since they change over time and may affect the
way interest rates respond to inflation.
37
Table 4.
Comparison of coefficients to those of other researchers.
di/dp
Researcher Name
dr/dp (di/dp-1)
>0
Mundell, Tobin
Darby
Gandolphi
Feldstein et al.
Levi, Makin
Fisher
Summers
Cargill
Tanzi
Makin
Wilcox
Calvert
<0
1.35a
1.22 to 1.35a,b
1.o8a
.857 to 1.33
. 8 to • 9
.29 to .86
.01 to 1.08
.782 to .879
1.06
.987
.915
.35
b
.22 to .35a'
.o8a
-.143 to .33
-.2 to -.1
-.71 to -.14
-.99 to .08
-.218 to -.121
.06
-.013
-.085
:Using marginal tax of 25%
Using marginal capital gains tax of 10%
The money model could be improved by including variables other than
historic money growth.
Some of the variables that could be included are
the GNP gap, the value of the dollar, and a proxy to control for
perceived risk in the banking system.
There may be other Federal Reserve actions that may affect interest
rates other than the growth of money.
Changing the time between Federal
Open Market Committee meetings and the publication of these minutes,
publishing targets for money growth, statements concerning future policy
and other policies may be important information not explicitly included
in this simple money model.
One of the problems of the Keynesian macroeconomic model this paper
is based on is its exclusion of foreign financial markets.
The
combination of foreign exchange rates, interest rates and other factors
could influence international flows of funds which could affect the U.S.
38
economy and financial markets.
These international variables could
become more important in the future as the U.S. share of world output
d~creases.
Continued research in this area would be interesting and potentially useful for government policy makers.
39
BIBLIOGRAPHY
40
BIBLIOGRAPHY
Ayanian, Robert. "Expectations, Taxes, and Interest: The Search for the
Darby Effect." American Economic Review 71 (September 1983): 762765.
Barro, Robert J. "Are Government Bonds Net Wealth?" Journal of Political Economy 82 (November/December 1974): 1094-1118.
Cargill, Thomas F. "Anticipated Price Changes and Nominal Interest
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(August 1976): 364-367.
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42
APPENDIX
43
DATA AND ESTIMATION TECHNIQUE
The data series for expected inflation came from the Livingston
survey.
Joseph Livingston, a financial reporter, collects economic
variable forecasts from many prominent economists with diverse backgrounds as part of a continuing survey~
The sampling frequency used in this paper is three months, so the
semiannual six-month forecasts collected by Livingston were linearly
interpolated for the second and fourth quarters.
The expected inflation
rate for the first quarter is assumed to be equal to the six-month
forecast made in December.
The second quarter expected inflation rate
used was then the linear interpolation of the previous December and
future June forecasts.
This interpolation procedure, along with the
facts that the original forecasts were made for six months rather than
three, and that the inflationary expectations of this select group of
economists may not be the same as those of most market participants,
will introduce random errors in measurement which will bias the
inflation coefficient towards zero.
The use of 6-month Treasury Bills
would have eliminated some of these problems, but that series doesn't
begin until 1959.
The proxy used for inflation uncertainty also came from the
Livingston survey.
The variability measure used was the standard
deviation of the inflation forecasts.
The variance of the forecasts was
also tried, but the results were insignificantly different.
This
44
variability measure is interpolated just as the inflation variable is,
and is therefore also biased towards zero because of random errors of
measurement.
The money surprise variable is defined to be the residuals from an
AR-5 model of Ml growth.
This is the simplest model yielding white
noise residuals, although the interest rate model is fairly insensitive
to other definitions such as MA-6 and MA-8.
The other monetary variable, money expected, is defined as the
forecast from the AR-5 model of money growth.
AR-5 model were estimated from the 1955-I to
The coefficients of the
1984~IV
period.
Ideally,
only the data available at a particular point in time should be used in
defining expectations, but in the interest of economy, it is assumed
that expectations of future money growth at any time were similar to
those estimated over the entire sample period.
The deficit variable is calculated as the cyclically adjusted
federal budget deficit as a percent of trend GNP, as calculated by the
Department of Commerce and reported in the "Survey of Current Business."
Several measures of federal financing were considered to be used in the
model, such as the change in the real debt and the change in the market
value of the real debt.
The change in the market value of the real debt
is very dependent on the interest rate and therefore endogenous.
It was
decided that the cyclically adjusted federal budget deficit as a percentage of trend GNP would be as interesting a variable as the others.
45
Estimation
The interest rate used in the model is a three-month average of the
three months' averages of new 91-day Treasury Bill yields at issue (U.S.
Department of Commerce, 1959, 1961, 1963, 1984).
Two-Stage Least Squares is used to introduce a variable to serve as
a proxy for the business cycle.
The first stage is the regression of
nominal GNP gap as a percent of trend GNP on all the other independent
variables and the lagged dependent variable.
The GNP gap and trend GNP
are from the "Survey of Current Business" (Deleeuw and Holloway, 1983).
The first attempt at estimating the model, using OLS, resulted in
heteroscedastic errors.
The Park-Glejser test was performed to test the
null hypothesis of no heteroscedasticity.
The t-ratio of the beta
coefficient is significant at greater than .001 probability, so the null
hypothesis is rejected.
This error problem is thought to originate from
the inflation variable since the variance of the errors is cqrrelated
with the level of expected inflation.
The reciprocal of several differ-
ent powers of the expected inflation rate were multiplied by the raw
data in an attempt to alleviate the problem.
The square root of the
expected inflation rate was finally chosen because it produced residuals
with fairly constant variance.
For the years where the expected inflation rate is less than one
percent, the heteroscedasticity correction was not applied, since
dividing by a very small number would produce outliers which would be
mistakenly given too great a weight in the regression.
46
The model was again estimated, using the data transformation noted
above, using OLS to examine the errors again.
The errors were auto-
regressive with the estimated p of .83 with a t-ratio of 16.22.
The
mean squared error was very significantly less (F ,
=249.41) than that
1 119
of the OLS residuals.
The AR-1 model of the OLS residuals was tested
against ARMA (2,0), (1,1), (1,2), and (2,2) models, with results of
F1 , 118=2.80, F1 , 118=1.55, F 2 , 117=1.75, and F3 , 116=1.19, respectively.
The coefficients of the autoregressive corrected model were similar
to those of the OLS except for the money surprise variable in Table 1.
The value of this variable increased from -.12 to -.05 and the t-ratio
rose from 2.82 to 3.08.